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math.CO2025
On Relative Ordered Turán Density
Dylan King, Bernard Lidický, Minghui Ouyang +3
For an ordered graph , denote the Turán density by . The relative Turán density, denoted by , is the supremum over such that every ordered grap…
math.CO2025
On possible uniform Turán densities
Dylan King, Simón Piga, Marcelo Sales +1
Given a family of -graphs , the uniform Turán density is defined as the infimum for which any sufficiently large uniform…
math.CO2025
Rainbow ErdÅs-Sós Conjectures
Nicholas Crawford, Dylan King, Sam Spiro
An edge colored graph is said to contain rainbow- if is a subgraph and every edge receives a different color. In 2007, Keevash, Mubayi, Sudakov, and Verstraëte introduced t…